Technique for achieving the full coding gain of encoded digital signals

ABSTRACT

In a telephone local loop transmission arrangement, data is communicated from the customer premises to the central office utilizing a multi-dimensional, passband signal illustratively at 480 kb/s. Specifically, the transmitted signal is encoded in a trellis code and precoded using a generalized partial response filter. The received signal is processed by a circuitry that implements a trellis decoding in combination with nonlinear filtering.

This application is a continuation-in-part of application Ser. No.415,939, filed on Oct. 2, 1989, and now being abandoned as of the filingdate hereof.

TECHNICAL FIELD

The present invention relates to data communication systems and, inparticular, to coding and equalization in such systems.

BACKGROUND OF THE INVENTION

A great deal of research has been done on a precoding technique, namely,generalized partial response signaling (GPRS). For details on GPRS, onecan refer to publications by M. Tomlinson, "New Automatic equalizeremploying modulo arithmetic," Electron. Lett., Vol. 7, nos. 5/6, Mar.1971, pages 138-139; H. Harashima and H. Miyakawa, "Matched-transmissiontechnique for channels with intersymbol interference," IEEE Trans.Commun., Vol. COM-20, August 1972, pages 774-780 and J. Mazo and J.Salz, "On the Transmitted Power in Generalized Partial Response," IEEETrans. Commun., Vol. Com-24, March 1976, pages 348-352, all of which arehereby incorporated by reference.

The GPRS technique enables one to prevent signals from being adverselyaffected by intersymbol interference caused by a signal transmissionthrough a channel having a finite memory and fixed characteristics.Knowing the impulse response of such a channel, one can design, inaccordance with GPRS, a nonlinear filter in the transmitter forprecoding the signals to be transmitted. This precoding compensates for,inter alia, intersymbol interference caused by the nonidealcharacteristics of the channel. GPRS, however, is not particularlyuseful for intersymbol interference compensation in actual communicationsystem applications. This stems from the fact that actual communicationchannels have a virtually infinite memory and time-variantcharacteristics, as opposed to the finite memory and fixedcharacteristics required by GPRS.

Much attention has been focused in recent years on signal-space codeswhich provide so-called "coding gain." Prominent among these are theso-called "trellis" codes described in such papers as G. Ungerboeck,"Channel Coding with Multilevel/Phase Signals," IEEE Trans. InformationTheory, IT-28, 1982, pages 55-67; A. R. Calderbank and N. J. A. Sloane,"A New Family of Codes for Dial-Up Voice Lines," Proc. IEEE GlobalTelecomm. Conf., November 1984, pages 20.2.1-20.2.4; A. R. Calderbankand N. J. A. Sloane, "Four-Dimensional Modulation With an Eight-StateTrellis Code," AT&T Technical Journal, Vol. 64, No. 5, May- June 1985,pages 1005-1018; A. R. Calderbank and N. J. A. Sloane, "AnEight-Dimensional Trellis Code," Proc. IEEE, Vol. 74, No. 5, May 1986,pages 757-759; and L-F Wei, "Rotationally Invariant ConvolutionalChannel Coding with Expanded Signal Space--Part I: 180 Degrees and PartII: Nonlinear Codes," IEEE J. Select. Areas Commun., Vol. SAC-2,September 1984, pages 659-686all of which are hereby incorporated byreference. Commercial use of these codes has, for the most part, beenconcentrated in voiceband data sets and other carrier data communicationsystems. The term "coding gain" refers to the increased performance of asystem resulting from the use of a particular code. It is defined as theamount by which the signal-to-noise ratio (SNR) may deteriorate for asystem utilizing that particular code before the bit error rate for thissystem equals that of the same system without using the code.

The trellis codes that have been developed to date provide full codinggain in the presence of "white" noise, i.e., noise that containscomponents of virtually every frequency in the spectrum. However, thenoise that appears in a received signal to be decoded is dependent uponthe characteristics of the channel through which the signal wastransmitted. Many communication channels, for example, a single two-wirepair or "local loop" of a telephone cable network that connects customerpremises to a central office, impart a received signal with non-white or"colored" noise. This being so, the resulting coding gain in systemsusing such channels is less than the full coding gain. Indeed, in manysystem applications the difference between the full coding gain and thatactually realized is significant. The failure to realize the full codinggain poses a problem with, for example, the proposed implementation ofthe Integrated Services Digital Network (ISDN). Relying on the fullcoding gain of, for example, the trellis code, ISDN purports to providehigh signal rates on the local loops while a nominal SNR is maintained.Not having this full coding gain realizable makes the implementation ofISDN extremely difficult. Accordingly, it is desirable to have such acoding gain fully or substantially realized.

SUMMARY OF THE INVENTION

The present invention increases the coding gain realizable for apredetermined code which provides a coding gain in the presence of whitenoise. The inventive technique requires first and second codingprocesses in a transmitter, and noise-whitening apparatus and nonlinearsignaling processing in the associated receiver. Specifically, the firstcoding process encodes input data with the predetermined code. Thenoise-whitening apparatus increases the realizable coding gain providedby the predetermined code. The second coding process compensates for theeffect of the noise-whitening apparatus which would otherwise degradesystem performance. Finally, the nonlinear signaling processing in thereceiver is associated with the second coding process and compensatesfor the operation of the same.

In each of three disclosed embodiments, the first coding process in thetransmitter is trellis coding. The whitening apparatus in the receiverincreases the realizable coding gain by ensuring that the noise at theinput to the trellis decoder is white. The second coding process in thetransmitter and the associated non-linear signaling processing is GPRSwhich is utilized to compensate for the undesirable effects of thenoise-whitening apparatus.

In particular, a first embodiment discloses a receiver arrangement inwhich the non-linear signaling processing follows the trellis decoding.Second and third embodiments disclose a different arrangement in whichthe non-linear signaling processing, by contrast, precedes the trellisdecoding, thereby advantageously simplifying the decoding process. Forfurther simplification thereof as illustrated in the third embodiment,one needs to provide more power, as compared with the first and secondembodiments, to carry out the second coding process in the transmitter.

BRIEF DESCRIPTION OF THE DRAWING

In the drawing,

FIG. 1 shows a block diagram of a duplex wideband network terminationincluding a first embodiment of an arrangement in accordance with thepresent invention, which is illustratively used in a telephone localloop data transmission scheme;

FIG. 2 shows the signal constellation used in a coder of the duplexwideband network termination of FIG. 1;

FIG. 3 is a table useful in explaining the operation of the coder withinthe duplex wideband network termination of FIG. 2;

FIG. 4 is a trellis diagram graphically depicting the so-calledconvolutional code used in the duplex wideband network termination ofFIG. 3;

FIG. 5 is a block diagram of a circuitry embodying the principles of thepresent invention, which precodes the signals to be transmitted in theduplex wideband network termination of FIG. 1;

FIG. 6 is a block diagram of a circuitry embodying the principles of thepresent invention, which performs equalization and decoding of receivedsignals in the duplex wideband network termination of FIG. 1;

FIG. 7 is a signal constellation appearing at the input of the decodingprocess performed by the circuitry of FIG. 6 using the signalconstellation of FIG. 2;

FIG. 8 is a block diagram of a circuitry embodying the principles of thepresent invention, which performs decoding of received signals in asecond embodiment of the present invention; and

FIG. 9 is a signal constellation appearing at the input of the decodingprocess performed by the circuitry of FIG. 8 using the signalconstellation of FIG. 2.

DETAILED DESCRIPTION

Three illustrative embodiments which implement the present invention aredescribed hereinbelow. Duplex wideband network termination (DWNT) 101 ofFIG. 1 includes a first embodiment of an arrangement in accordance withthe present invention. DWNT 101 is illustratively used to implement ISDNvia a single two-wire pair or "local loop" between customer premises anda central office (not shown). In particular, ISDN would provide acustomer with duplex, i.e., simultaneous two-directional, digitaltransmission capability at a speed ranging from the so-called ISDN"basic" (2B+D) rate (with framing, maintenance and control bits) or 160kb/s up to the so-called "primary" (23B+D) rate (again with framing,maintenance and control bits) up to 1.544 Mb/s and even beyond.

Specifically, data from various digital signal sources, such as a simplecomputer terminal, a cluster controller, a minicomputer, a digital videosignal source, etc., on the customer premises is applied to amultiplexer/demultiplexer (mux/demux) 50 within DWNT 101. The latterembeds the signals from these sources in an outbound 480 kb/s datastream on lead 54. That data stream could be formatted, for example,using an ISDN-type format, although an ISDN standard for 480 kb/s hasnot yet been adopted. The data stream on lead 54 is input to theaforementioned DWNT 101, which communicates its input data to a centraloffice via a two-wire local loop 60 of a maximum length of 18 kft perISDN standards. Within the central office, the bit stream is recoveredfrom the transmitted line signal by a duplex wideband line termination(DWLT) (not shown) associated with DWNT 101 and, after beingdemultiplexed, is passed to a digital switch. The latter may be, forexample, a 5ESS switch manufactured by AT&T which includes softwarewhich processes the framing, maintenance, and/or control informationcarried in the so-called "D" channel of the ISDN signal.

DWNT 101 and the associated DWLT are complementary in their function.For a given direction of transmission, one of them performs as atransmitter and the other as a receiver. Thus, data from the digitalswitch destined for the customer premises, also at 480 kb/s, is passedto the DWLT which generates a line signal representing that data. Theline signal is then transmitted over local loop 60 to DWNT 101 whichthen recovers the data and passes it to the customer premises. Indeed,the circuitry within DWNT 101 and the associated DWLT is very similar tothat in the other and, as far as the generation and processing of linesignals is concerned, they may be regarded as being identical.

In general, a DWNT embodying the principles of the present invention canbe manufactured with the capability of operating over a range of bitrates, with the bit rate actually used at a particular time being eitherselected manually via, say, a front panel control or adaptively by theDWNT/DWLT pair themselves during their start-up sequence.

Referring to FIG. 1, specifically, the aforementioned 480 kb/s signal onlead 54 is received by transmitter section 121 within DWNT 101 and isapplied therewithin to a scrambler 112. The latter, in a conventionalfashion, randomizes the data so as to eliminate the possibilities ofgenerating tones within the line signal ultimately to be generated.Scrambler 112 may be, for example, of the type shown in U.S. Pat. No.3,515,805 issued June 2, 1970, to R. Fracassi, and U.S. Pat. No.4,304,962 issued Dec. 8, 1981, to R. Fracassi, et al. Scramblers of thistype are also described in polynomial form in CCITT V.32 Recommendation,"A Family of 2-Wire, Duplex Modems Operating at Data Signaling Rates ofup to 9600 Bit/s for Use on the General Switched Telephone Network andon Leased Telephone-Type Circuits, " Red Book, Volume VIII--FascicleVIII-1, Data Communications Over the Telephone Network, VIII^(th)Plenary Assembly, Malaga-Torremolinos, pp. 221-238, Oct. 8-19, 1984. Theoutput bits of scrambler 112, still at a 480 kb/s rate, are thereuponconverted to six-bit words by serial-to-parallel (S/P) converter 113,the bits of each such word being denoted X1 through X6. These six-bitwords, occurring at 480,000/6=80,000 per second, are thereupon mapped bya coder 114 into a stream of symbols--one symbol for each word--yieldinga symbol rate of 80 kilobaud.

Specifically, coder 114 expands the six-bit words received fromserial-to-parallel converter 113 into seven-bit words comprised of bitsY0 through Y6. Bits Y0, Y1 and Y2 are generated by trellis coder 140within coder 114 in response to bits X1 and X2, as described in furtherdetail hereinbelow, while bits Y3 through Y6 are identical to bits X3through X6.

At this point, it should be noted that DWNT 101 operates in two modes,namely--a training mode and a normal operation mode. Generally thetraining mode, during which tap coefficients of adaptive filters in DWNT101 are initialized, precedes the normal operation mode. The change fromone mode to the other is illustratively achieved by means of switches.Each of these switches has two positions, position 1 being for thenormal operation mode and position 2 being for the training mode.Toggling from one mode to the other is in response to a control signalA.

In the normal operation mode, switches 130 a through g respectivelycouple bits Y0 through Y6 to bit-to-symbol converter 177. However, inresponse to the aforementioned control signal A, switches 130 a throughg couple initialization bits IY0 through IY6, instead, to thatbit-to-symbol converter to facilitate the initialization of the tapcoefficients in a manner to be described. Bits IY0-IY6 are uncodedtraining bits supplied by training sequence generator 139 ofconventional design.

Bit-to-symbol converter 177 maps each of the 2⁷ or 128 differentcombinations of its input bit values into one of 128 two-dimensionalsymbols in a predetermined constellation. One illustrative constellationis shown in FIG. 2.

More specifically, each of the 128 symbols of the constellation in FIG.2 is assigned to a particular one of eight partitions, or subsets,labelled a through h. In the normal operation mode, the values of bitsY0, Y1 and Y2 identify, in accordance with the assignment scheme shownin FIG. 3, the particular one of the eight subsets from which the symbolcurrently being identified is to come while the values of bits Y3through Y6 identify a particular one of the sixteen symbols within theidentified subset.

The assignment of each of the sixteen different combinations of thevalues of bits Y3 through Y6 to a particular symbol within theidentified subset can be arbitrary. However, by appropriate choice of a)the so-called trellis code used by trellis coder 140 to generate bitsY0, Y1 and Y2, b) the constellation, and c) the partitioning of theconstellation into particular subsets, so-called "coding gain" isachieved. Such coding gain manifests itself in the form of enhancedreceiver immunity to channel noise as compared to the channel noiseimmunity of an "uncoded" system in which each symbol of (in thisexample) a 64-symbol constellation would be used to directly represent adifferent one of the 2⁶ =64 different combinations of the values of bitsX1 through X6.

A circuit embodiment of trellis coder 140 is explicity shown in FIG. 1.Specifically, trellis coder 140 is a finite-state machine which includesdelay elements 181, 182 and 183 and exclusive-OR gates 184 and 185. Eachof the delay elements imparts a symbol interval delay of T seconds toits inputs, where T is the reciprocal of the symbol rate, i.e.,T=1/80,000 and is commonly referred to as the symbol interval. Theinputs of exclusive-OR gate 184 are bit X1 and the output of delayelement 181. The inputs of exclusive-OR gate 185 are bit X2 and theoutput of delay element 182. Delay element 181 receives as its input theoutput of delay element 183; delay element 182 receives as its input theoutput of exclusive -OR gate 184; and delay element 183 receives as itsinput the output of exclusive-OR gate 185. The output of delay element183 also serves as output bit YO.

The underlying premise of trellis coding is that, at any point in time,only the symbols in particular subsets of the constellation are allowedto be transmitted, and these subsets are determined by the "state" ofthe trellis coder. The trellis diagram of FIG. 4, for example,represents the operation of trellis coder 140. As shown in FIG. 4,trellis coder 140 has eight "states", binary 000 through binary 111,given by the values of the bits currently stored in delay elements 181,182 and 183. Thus, for example, if the coder is in state 001, this meansthat delay elements 181 and 182 each currently hold a logic "0" anddelay element 183 currently holds a logic "1". The two sets ofvertically aligned points in FIG. 4 represent the eight possible coderstates at each of two successive time intervals. One of these sets isdesignated as current state and the other set is designated as nextstate. The lines or edges, connecting various pairs of states indicatethe possible state transitions. Thus, for example, it is possible forthe coder to transition from state 010 to state 001 but not to state100.

Each of the connecting lines in FIG. 4 bears a label indicating whichsubset the symbol being generated is to come from. Thus, continuing theexample above, assume that the current state of the coder--i.e., thecontents of delay elements 181, 182 and 183, is 010 and that, after thenext six-bit word is supplied by serial-to-parallel converter 113, thenew state is state 001. This means that the next symbol to be output isto come from subset "a" since the line connecting state 001 in the leftcolumn to state 111 in the right column is so labeled. With the codernow in state 001, the next symbol to be output will come from one of thesubsets "e", "f", "g" or "h", depending on the upcoming values of X1 andX2.

Referring again to FIG. 1, bit-to-symbol converter 177 respectivelyprovides on its output leads 102 and 103 the in-phase and quadrature-phase components of the symbol identified by bits Y0-Y6 or bitsIY0-IY6. In terms of the constellation diagram of FIG. 2, thesecomponents represent the "x" and "y" components of the identifiedsymbol. Leads 102 and 103 are extended in the normal operation mode togeneralized partial response precoder (GPRP) 179 via the setting ofswitches 131 and 133 to their respective positions 1. Like switches 130a-g described before, switches 131 and 133 change to their respectivepositions 2 in response to the aforementioned control signal A,resulting in the training mode. That is, in the training mode, switches131 and 133 short, respectively, lead 102 to lead 105 and lead 103 tolead 107. As a result, GPRP 179 is illustratively bypassed.

GPRP 179 performs GPRS precoding which prevents certain intersymbolinterference from being injected into a received signal. FIG. 5 showsGPRP 179 which comprises subtracter 501, subtracter 502, nonlinearfilter 505, nonlinear filter 506 and Mth-order transversal filter 509.Subtracter 501 takes in an output of Mth-order transversal filter 509,namely S_(n) ^(x), which is to be described, as one input, and theinphase component on lead 102 as the other. This subtracter subtractsthe value of S_(n) ^(x) from the value of the inphase component. Theresulting value, α^(x), is represented by a signal which is applied atthe input of nonlinear filter 505.

This filter in general performs a nonlinear function F on its inputsignal whose value is, say, α. The value of the output signal generatedby the filter is thus F(α), which is equal to α if -L≦α≦L; otherwise αis reduced to this range of -L to L by algebraically adding orsubtracting an appropriate multiple of 2L and the result becomes F(α).

In this instance, since the input value is α^(x), nonlinear filter 505thus generates on lead 104 an output signal which represents F(α^(x)).In addition, nonlinear filter 505 effects a bound of L on the absolutevalue of its output signal, thereby limiting the power of same. Inaccordance with GPRS, the value of L is defined to be 0.5 C^(x) I^(x)where C^(x) is the number of possible levels assumable by the "x"component of a symbol in the constellation, and I^(x) is the intersymboldistance along the X-axis. This resulting value of L is hereinafterreferred to as the "GPRS bound". As illustratively shown in FIG. 2, the"x" component of a symbol can assume 12 possible levels, and theintersymbol distance is two units along the X-axis. Therefore, L=12 andthe GPRS bound in this embodiment.

The signal on lead 104 at the n^(th) transmission interval is denotedG_(n) ^(x) and is processed with another signal, G_(n) ^(y), by complexshaping filter 116 in a manner to be described. G_(n) ^(y), like G_(n)^(x), is formed by first having subtracter 502 subtract the value ofS_(n) ^(y), which is another output of Mth-order transversal filter 509,from the value of quadrature component on lead 103. The resulting value,α^(y), is represented by a signal which is input to nonlinear filter506. The latter is identical to nonlinear filter 505 and thus provideson lead 106 G_(n) ^(y) whose value is F (α^(y)). Even though the GPRSbound value of L associated with nonlinear filter 506 is now defined as0.5 C^(y) I^(y) (where C^(y) is the number of possible levels assumableby the "y" component of a symbol in the constellation, and I^(y) is theintersymbol distance along the Y-axis), as it can be seen from FIG. 2,this value remains 12 in this particular embodiment.

G_(n) ^(x) and G_(n) ^(y) are also fed back to Mth-order transversalfilter 509 of conventional design, which generates as its outputs S_(n)^(x) and S_(n) ^(y) on, respectively, leads 511 and 512 in accordancewith the relations:

    S.sub.n.sup.x =Re(P.sub.n.sup.T b.sub.n), and

    S.sub.n.sup.y= Im(P.sub.n.sup.T b.sub.n).

In these expressions, b_(n) is a (M×1) matrix, or vector, comprised ofthe M most recent inputs of transversal filter 509 which are representedby complex numbers. That is, ##EQU1## where i=√-1 and M is a selectedfinite integer. The value of M is intrinsic to the characteristics ofthe channel used. In the present embodiment, the illustrative channelbeing a conventional 18 kft, 24 guage two-wire local loop with no bridgetap, the value of M associated therewith is experimentally determined tobe 7.

P_(n) is a (M×1) vector or matrix comprised of an ensemble of M tapcoefficients associated with transversal filter 509. That is, ##EQU2##where p_(n),r¹ +i p_(n),im¹ i p_(n),r₂ +i p_(n),im². . . p_(n),r^(M) +ip_(n),im^(M) are complex numbers used as the respective M tapcoefficients at the n^(th) transmission interval. As to be describedhereinbelow, these tap coefficients are supplied from decision outputcircuitry 150. (The superscript "T" used in the above expressionsindicates the matrix transpose operation wherein (M×1) vector P_(n) istransposed into (1×M) vector for the purpose of matrix multiplication.)In addition, Re is an operation that eliminates the imaginary componentof a complex number and Im is another operation that eliminates the realcomponent of same. For example, Re(2+i3)=2 and Im(2+i3)=3.

In the course of the precoding process, GPRP 179 renders, in aconventional manner, more different values assumble by each of G_(n)^(x) and G_(n) ^(y) than each of the respective in-phase andquadrature-phase component inputs. This being so, G_(n) ^(x) and G_(n)^(y) respectively represent more "x" and "y" components of symbols thanthose component inputs. That is, after the precoding process, G_(n) ^(x)and G_(n) ^(y) combinedly represent more symbols to be transmitted thanthe symbols defined in the constellation of FIG. 2. Equivalently stated,the precoding process effects an expansion of the constellation of FIG.2.

The signals on, respectively, lead 105 and lead 107 are applied tocomplex shaping filter 116, which generates a passband signal which isillustratively a so-called "carrierless AM/PM" signal.

Implementationally, complex shaping filter 116 is, illustratively,comprised of two finite-impulse-response digital filters of conventionaldesign-in-phase filter 191 and quadrature phase filter 192--which filterthe signals on leads 105 and 107, respectively. Each of these filters isillustratively realized as a transversal filter. Filters 191 and 192differ from each other only in that their phase characteristics areoffset from one another by π/2. This phase difference enables thereceiver section of the associated DWLT to separately reconstruct thesignals on leads 105 and 107. The outputs of filters 191 and 192 arecombined in an adder 193 to provide a digital version of the desiredoutbound line signal.

It is important to note that the approach taken within complex shapingfilter 116 for generating a passband signal in response to thetwo-dimensional symbols represented by the signals on leads 105 and 107is different from the modulation typically used in, for example,voiceband modems, such as quadrature amplitude modulation, or QAM. Inthe latter, specifically, an explicit or implicit (depending on theimplementation) rotation of the symbols by a carrier-frequency-dependentangle occurs. However no such explicit or implicit rotation is performedwith carrierless AM/PM. This is significant because unless there happensto be an integral relationship between the carrier frequency and thesymbol interval T (which is not likely to be the case if the carrierfrequency and symbol interval values are chosen to optimize theperformance of the transmission scheme as a whole), the aforementionedrotation operation will involve a non-trivial multiplication, therebyadding not insignificantly to the cost of the transmitter section. Afurther advantage is that carrierless AM/PM is more simply processed atthe receiver than, for example, QAM. Additionally, carrierless AM/PM ispotentially more robust in the presence of non-linearities, such as maybe introduced in the analog-to-digital conversion performed in thereceiver.

The output of complex shaping filter 116 is converted to analog form byD/A converter 117 whose output is then passed through low pass filter118 to remove the higher-frequency images of the desired signal. Hybrid126 thereupon extends the resulting outgoing line signal appearing ontransmitter section output lead 119 to its two-wire side and thence ontolocal loop 60.

Turning now to the inbound transmission direction, the line signalgenerated on local loop 60 by the associated DWLT is received by hybrid126 which routes that signal on to receiver section 123 and, moreparticularly, low-pass filter 142 thereof. The latter filters out energyin the received signal at frequencies nominally above the spectrum ofthe transmitted signal. The resulting filtered signal passes to gaincontrol circuit 147 which is programmable to adjust the gain imparted toits input so as to make maximum use of the precision of A/D converter148 which follows. The gain of circuit 147 is set, based on the level ofits input signal during modem initialization or training, and isthereafter held at the initially set value, in accordance with standardpractice for echo-canceller-based data communications.

Receiver section 123 further includes a clock 143, which generates apredetermined number of clock pulses every T seconds on lead 144. Theseare received by receiver timing generator 145, which counts the pulseson lead 144 and generates timing signals on a number of output leads tocontrol the sequencing of the various signal processing functions withinthe receiver. One of these leads, shown explicitly, is lead 146. Thelatter extends pulses to A/D converter 148 at a rate which causes theconverter to generate samples of the received signal, referred to as"line samples", at 3/T samples per second on output lead 149.

Each of the samples on lead 149 includes an echo component that isdominantly comprised of the so-called "near echo" and secondarilycomprised of the so-called "far echo." The near echo results from energythat "leaks" from transmitter output lead 119 through hybrid 126 toreceiver input lead 141, and the far echo arises from reflections of thetransmitted signal from the transmission channel. Echo canceller 127, inresponse to the symbols represented on leads 105 and 107, generatesdigital samples, each representing the echo component of a respectiveone of the samples on lead 149. This echo replica signal is subtractedfrom the samples on lead 149 in subtracter 128 to provide anecho-compensated signal on lead 152.

The echo-compensated signal on lead 152, in addition to being furtherprocessed as described below to recover the bit stream communicated frommux/demux 50 is also used by echo canceller 127 as an error signal inresponse to which it adapts its transfer function in such a way as tominimize the residual echo component of the signal on lead 152. Echocanceller 127 is, illustratively, of the type shown in U.S. Pat. No.4,464,545 issued Aug. 7, 1984, to J. Werner, hereby incorporated byreference. Among its more significant parameters, echo canceller 127illustratively has a memory span of 40 symbols, adaptation step size of2⁻²⁰ and arithmetic precision of 26 bits using fixed point arithmetic.These parameters are expected to provide at least 65 dB of near echoattenuation, this being the likely minimum necessary level of near echocancellation for this application.

The line samples on subtracter output lead 152 generated during then^(th) receiver symbol interval are denoted r_(1n), r_(2n) and r_(3n).These three line samples are passed to decision output circuitry 150 forfurther processing to be described hereinbelow. It may be noted at thispoint, however, that line samples r_(1n), r_(2n) and r_(3n) are alsoapplied to timing recovery circuit 153, which uses them to controltiming generator 145. (Other types of timing recovery schemes, such asthose employing out-of-band tones or other out-of-band signals mightalternatively be used.) Although, as noted hereinbefore, the associatedDWLT may be regarded as substantially identical to DWNT 101, one smalldifference is that DWLT, illustratively, does not include a timingrecovery circuit corresponding to timing recovery circuit 153. Rather,the receiver timing generator in that DWLT operates exclusively inresponse to the clock therein, the latter, in turn, being controlled bya network timing signal provided from within the central office. Thefrequency of the clock of the DWLT thus becomes the controllingfrequency for the operations of both the transmitter and receiversections of both DWNT 101 and the associated DWLT. As previously noted,line samples r_(1n), r_(2n) and r_(3n) on lead 152 are further processedby decision output circuitry 150.

Turning to FIG. 6, decision output circuitry 150 comprises T/3 linearequalizer 607, M+1st-order transversal filter 619, decision and errorsignal generators 609 and 640, and switches 631, 635, 638 and 639.Specifically, T/3 linear equalizer 607 eliminates from the line samplesthe so-called "precursors", the intersymbol interference caused by localloop 60. To this end, line samples r_(1n), r_(2n) and r_(3n) are appliedto linear equalizer 607 which is of conventional design and may be, forexample, of the type disclosed in U.S. Pat. No. 3,868,603 issued Feb.25, 1975, to Guidoux, hereby incorporated by reference. Since linearequalizer 607 receives and processes more than one input for each symbolinterval, it is referred to as a "fractionally spaced" equalizer. It is,more specifically, referred to as a T/3 type of fractionally spacedequalizer since it receives and processes inputs at a rate of three persymbol interval, and thus has a so-called "tap" spacing of T/3. Afractionally-spaced linear equalizer is advantageous as compared to aso-called symbol-interval-spaced equalizer because, for example, it isinsensitive to phase distortion in the channel and to the time intervalsor epochs during which the successive line samples are formed.

The output of T/3 linear equalizer 607 on lead 611 is generated once persymbol interval and is comprised of the real and imaginary components,respectively, eq_(n) and eq_(n) * of a complex signal EQ_(n). At thispoint, it should be noted that decision output circuitry 150 of FIG. 1operates in concert with the rest of the circuitry of DWNT 101 in eitherof the normal operation mode and training mode in response to theaforementioned control signal A.

The following delineates the process of decision output circuitry 150 inthe normal operation mode. In this mode, T/3 linear equalizer 607 andM+1st-order transversal filter 619 are connected to decision and errorsignal generator 609. Specifically, switch 639 connects output lead 613of transversal filter 619 to input lead 614 of decoding circuitry 660within decision and error signal generator 609; switch 638 couples anerror signal E_(n) ² from the generator to transversal filter 619;switch 635 couples EQ_(n) on lead 611 to buffer 621 within thegenerator; and switch 631 couples an error signal E_(n) ¹ from thegenerator to linear equalizer 607.

E_(n) ¹ is indicative of the difference in value between the outputsignal of linear equalizer 607 and decisions thereafter made in thereceiver as to what the transmitted symbols actually were. A particularone of these decisions provided at the output of decision and errorsignal generator 609 during the n^(th) receiver symbol interval is acomplex signal X_(n-K) on lead 161 having, respectively, the real andimaginary components x_(n-K) and x_(n-K) *. K is an experimentallydetermined constant delay needed by decoder 603 to decode a particulartrellis code by the conventional Viterbi algorithm. (In the presentembodiment, the trellis code used in coder 140 experimentally requiresK=15.)

As a result of the delay in decoder 603, the error signal E_(n) ¹generated by decision and error signal generator 609 involves storingEQ_(n) in buffer 621 for K symbol intervals so that the current outputthereof is a complex signal EQ_(n-K) which was the output from linearequalizer 607 K symbol intervals ago. The complex signal EQ_(n-K) hasreal and imaginary components, respectively, eq_(n-K) and eq_(n-K) *.The formation of E_(n) ¹ also involves processing X_(n-K) on lead 161using GPRP 629 which is structurally identical to GPRP 179 of FIG. 1 asdescribed before. The output of GPRP 629 is a complex signal J_(n-K),having real and imaginary components, respectively, J_(n-K) and J_(n-K)*. Substracter 615 provides the complex error signal E_(n) ¹ having realand imaginary components, respectively, e_(n) ¹ and e_(n) ^(1*), wheree_(n) ¹ =(eq_(n-K) -j_(n-K)) and e_(n) ^(1*) =(eq_(n-K) *-J_(n-K) *).This error signal E_(n) ¹ is supplied to linear equalizer 607 for thepurpose of coefficient updating in a conventional manner.

Returning briefly to the description of EQ_(n) on lead 611, the noisethat appears in EQ_(n) is of the type characteristic of the channel overwhich the symbols were transmitted. Illustratively, the channel being alocal loop, like many other channels, contributes to the transmittedsymbols mostly the so-called "colored", rather than "white", noisearising from cross-talk within the transmission cable.

However, the trellis codes that have been developed to date, includingfor example, the code represented by the trellis diagram of FIG. 4, areknown to provide coding gain in the presence of "white" noise.

This being so, in order to substantially realize the full coding gain ofthe trellis code used, the noise that appears in trellis-coded signalsto be processed by decoder 603 is, by design, in accordance with thepresent invention, whitened before being decoded.

To this end, EQ_(n) on lead 611 is input to conventional M+1st-ordertransversal filter 619 which whitens the noise that appears therein.Thus transversal filter 619 provides onto lead 613 a complex signalZ_(n) which is destined for decoder 603, and which has a noise componentensured to be white.

Specifically, Z_(n) has, respectively, real and imaginary componentsz_(n) and z_(n) *. Transversal filter 619 generates its output byforming linear combinations of the filter input components in accordancewith the relations:

    z.sub.n =eq.sub.n +Re(P.sub.n.sup.T u.sub.n), and

    z.sub.n *=eq.sub.n *+Im(P.sub.n.sup.T u.sub.n).

In these expressions u_(n) is a (M×1) matrix, or vector, comprised ofthe M most recent complex output samples of linear equalizer 607. Thatis, ##EQU3## where M and P_(n) are described hereinbefore.

It should be noted at this point that the above-described whiteningprocess performed by transversal filter 619 would normally haveintroduced, as a concomitant, intersymbol interference or specificallythe so-called "post-cursors", into its output signal Z_(n). Based on thepresent design of the "whitening" filter--transversal filter 619, thegeneration of the "post-cursors" is prevented, in accordance with thepresent invention, using the aforementioned GPRS precoding in thetransmitter. Specifically, the "whitening" filter is designed, asrequired by the GPRS precoding, to be of finite memory; that is, ittakes in at a time a finite number--M--of the most recent inputsthereto. As described hereinbefore, GPRP 179 in transmitter section 121performs such a precoding. This precoding further entails transportingfrom transversal filter 619 once per symbol interval a copy of the tapcoefficients of P_(n), which characterizes that filter, via internal bus187 to GPRP 179 for use in the transversal filter therein. Thisprovision of the tap coefficients from transversal filter 619 in thereceiver of DWNT 101 is based upon a reasonable assumption that thecharacteristics of the illustrative channel--local loop 60--arenon-directional. That is, the channel characteristics remain the same ineither of the transmit direction or the receive direction of thechannel. Otherwise, a copy of the tap coefficients would be supplied toGPRP 179, via local loop 60, from the counterpart of transversal filter619 in the receiver of the associated DWLT, instead.

It should also be noted that in the present illustration, transversalfilter 619 and transversal filters in all the GPRPs, use the same copyof P_(n). This includes GPRP 629 which takes in a copy of P_(n) viainternal bus 618. This being so, it advantageously facilitates theadaptive process in DWNT 101 because during each symbol interval, onlyone set of coefficients needs to be updated.

The values of the coefficients of P_(n) are updated in transversalfilter 619 in a conventional manner, based on the complex error signalE_(n) ² on lead 617 input thereto. The initialization of all the tapcoefficients in DWNT 101 including those of transversal filter 619 andlinear equalizer 607 is to be described hereinbelow.

The complex error signal E_(n) ² is produced by decision and errorsignal generator 609. The production involves storing Z_(n) on outputlead 620 which is connected to input lead 614 of decoding circuitry 660therein. Buffer 633, which is identical to buffer 621 as describedbefore, stores Z_(n) for K symbol intervals. The output of buffer 633 isthus a delayed version of Z_(n) which is denoted Z_(n-K). Subtracter 637takes in Z_(n-K) as one input and as the other input a second signal onlead 630 which is connected to output lead 625 of decoder 603. Thissecond signal is denoted D_(n-K) and is the current output of decoder603. Subtracter 637 thus subtracts the real and imaginary components ofD_(n-K) from the corresponding components of Z_(n-K) and provides onlead 617 complex error signal E_(n) ².

Z_(n) on lead 614 is fed to decoding circuitry 660 wherein decoder 603performs a trellis decoding on Z_(n) with the Viterbi algorithm ofconventional design. Details on the Viterbi algorithm can be referred toG. Ungerboeck, "Channel Coding With Expanded Signal Sets," IEEE Trans.on Information Theory, Vol. IT-28, No. 1, January, 1982, and G.Ungerboeck, "Trellis-Coded Modulation With Redundant Signal Sets, Part Iand II, " Communications Magazine, IEEE Communication Society, February,1987. Also of interest is the discussion in G. D. Forney, "The ViterbiAlgorithm", Proceedings of the IEEE, Vol. 761, pp. 268-278, March, 1973.

Based on the input to decoder 603, the knowledge of the trellis codeused in coder 140 and a predetermined configuration of so-called"allowed symbols", the Viterbi algorithm generates with a delay of Ksymbol intervals the "maximum-likelihood" decisions as to what the mostlikely allowed symbols that input represents. The predeterminedconfiguration of the allowed symbols describes the arrangement ofsymbols that can possibly appear at decoder 603. It should be pointedout that in the present embodiment this predetermined configuration isdifferent from, for example, FIG. 2 which is the constellation used inthe transmitter and to which the Viterbi algorithm normally refers. Infact, it can be shown that FIG. 7 depicts such a configuration.

As a result of the expansion of the constellation of FIG. 2 caused bythe GPRS precoding as noted previously, FIG. 7 is realized to be anexpanded version of FIG. 2. Specifically, FIG. 7 has in the center theconstellation of FIG. 2 enclosed in a dashed cruciform box, andsurrounding the cruciform box truncated constellations of FIG. 2, ormore specifically, four halves and four quarters of FIG. 2 as defined bydashed lines. The existence of the truncated constellations is aconsequence of the power limiting effect caused by the nonlinear filtersof the GPRP. Otherwise, were there no power limit, FIG. 7 would becomprised of a virtually limitless number of complete constellations ofFIG. 2 repeated throughout the X-Y plane.

As described hereinbefore, those nonlinear filters of the GPRP, forexample, nonlinear filter 505, limit the values of the "x" and "y"components of the channel symbols to be transmitted between -L and L,where L=12--the GPRS bound--in this illustrative embodiment. This inturn limits the number of levels of values that can be individuallyassumed by the "x" and "y" components of the allowed symbols of FIG. 7.The resulting number of levels turns out to be 2L. This being so, FIG. 7takes the form of a centered truncated square of 2L levels by 2L levelsof the otherwise X-Y plane comprised of a virtually limitless number ofthe constellations of FIG. 2 as in the power-unlimited case.

An individual one of the aforementioned "maximum likelihood" decisionsis denoted D_(n-K) and is provided by decoder 603 on to lead 625 whichextends to nonlinear filter 627. It can be shown mathematically thatnonlinear filter 627, which is identical to nonlinear filter 505 asdescribed hereinbefore, recovers symbols representing Y0 through Y6based on the maximum likelihood decisions. An individual one of signalsidentifying those symbols, namely X_(n-K), is provided by nonlinearfilter 627 onto lead 161.

The foregoing sets forth the normal operation of decision outputcircuitry 150. However, in response to the control signal A, asmentioned before, circuitry 150 switches to the training mode forinitializing the tap coefficients of the adaptive filters therein.

The training process involves connecting T/3 linear equalizer 607 andM+1st-order transversal filter 619 to decision and error signalgenerator 640 and dissociating them from decision and error signalgenerator 609. Specifically, switches 631, 635, 638 and 639 altogetherswitch to respective positions 2 in response to the control signal A. Bydoing so, switch 631 couples an initialization error signal IE_(n) ¹from decision and error signal generator 640 to T/3 linear equalizer607; switch 635 couples EQ_(n) on lead 611 to subtracter 651 within thegenerator; switch 638 couples another initialization error signal IE_(n)² from the generator to transversal filter 619; and switch 639 connectstransversal filter 619 to subtracter 641 within the generator. Theresulting arrangement of decision output circuitry 150 is a conventionaladaptive decision feedback equalizer where linear equalizer 607 togetherwith transversal filter 619 becomes the so-called "feedforward filter";Mth-order transversal filter 653 within decision and error signalgenerator 640 becomes the so-called "decision feedback filter;" andslicer 643 becomes the so-called "decision generator" associatedtherewith.

During the training process, all the tap coefficients in decision outputcircuitry 150 including those of Mth-order transversal filter 619 areinitially set to zero. The tap coefficients of linear equalizer 607 andtransversal filter 619 are thereafter optimally adjusted in aconventional manner, based on, respectively, the complex initializationerror signals IE₂ ¹ and IE_(n) ². The resulting set of tap coefficientsassociated with transversal filter 619 is transported via internalbuses, as mentioned before, to all the GPRPs in DWNT 101 for use intheir respective transversal filters.

Subtracter 651 provides IE_(n) ¹ by subtracting the real and imaginarycomponents of EQ_(n), which are now associated with the aforementionedinitialization input bits IY0-IY6 in the transmitter, from thecorresponding components of SL_(n). The latter is, as describedhereinbelow, the output of conventional slicer 643. IE_(n) ² is providedby substracter 649 which subtracts the real and imaginary components ofSL_(n) from the corresponding components of a complex signal Q_(n).Subtracter 647 generates the complex signal Q_(n) by subtracting thereal and imaginary components of Z_(n), which is now associated with theaforementioned initialization input bits IY0-IY6, from the correspondingcomponents of a complex signal H_(n). This last complex signal isprovided through processing SL_(n) using transversal filter 645 which isidentical to transversal filter 509 of FIG. 5 as described before. Thetap coefficients of transversal filter 645 are supplied by transversalfilter 619 via internal bus 653.

Slicer 643 provides in a conventional manner at its output theaforementioned complex signal SL_(n) which is the quantized version of acomplex signal SU_(n) input thereto. Subtracter 641 generates thecomplex signal SU_(n) by subtracting the real and imaginary componentsof H_(n) from the corresponding components of Z_(n).

Returning to FIG. 1, the aforementioned symbol-identifying signals onlead 161 provided by decision output circuitry 150 are input tosymbol-to-bit-converter 162. This converter performs the inversefunction of bit-to-symbol converter 177, thereby recovering the valuesof bits Y0 through Y6. Since the values of Y0 through Y6 are identicalto the values of X0 through X6, these values can be directly passedthrough parallel-to-serial converter 164 and descrambler 165 in order toprovide the bit stream that was input to the associated DWLT.

In order to advantageously simplify the decoding process as illustratedin the first embodiment which is fully described hereinbefore, a secondembodiment is included. This second embodiment is identical to the firstembodiment except for the decoding circuitry in decision outputcircuitry 150 of FIG. 6. Specifically, in the second embodiment,decoding circuitry 880 of FIG. 8 replaces decoding circuitry 660 in FIG.6.

A closer look at FIG. 8 reveals that unlike decoding circuitry 660 inthe first embodiment, decoding circuitry 880 has nonlinear filter 827preceding decoder 803. Nonlinear filter 827 is structurally identical tononlinear filter 627 as described before. After processing Z_(n) oninput lead 614, nonlinear filter 627 provides a complex signal NF_(n) onto leads 810 and 620.

Decoder 803, like decoder 603, implements the Viterbi algorithm on itsinput NF_(n) on lead 810. Similarly, based on the knowledge of thetrellis code used in coder 140 and a predetermined configuration of theallowed symbols at decoder 803, the Viterbi algorithm generates with adelay of K symbol intervals the maximumlikelihood decisions as to whatthe most likely allowed symbols that NF_(n) represents. An individualone of the maximum-likelihood decisions is, now, denoted X_(n-K) and isprovided by decoder 803 on to leads 630 and 161.

In accordance with GPRS, the aforementioned predetermined configurationof allowed symbols at decoder 803 is, in fact, represented by FIG. 2.This being so, the decoding process in the present illustrativeembodiment is advantageously simpler than that in the first embodiment.This stems from the fact that FIG. 2 is comprised of fewer allowedsymbols than FIG. 7 of the first embodiment. Thus, the decoding processin the present embodiment results in fewer calculations in theimplementation of the Viterbi algorithm. These calculations of, forexample, figuring out squared Euclidean distances between individualallowed symbols and the symbol represented by a decoder input enable thealgorithm to make a plurality of the so-called "tentative" decisions asto, in this case, what symbol was generated by bit-to-symbol converter177.

There are inputs of decoder 803 representing symbols which lie outsidethe boundary of FIG. 2, the boundary being defined by the dash-dottedline. Based on such a decoder input, the tentative decisions generatedby the Viterbi algorithm would be ones of the allowed symbols next tothe boundary. However, it can be shown that in this particularembodiment, not all of such "tentative" decisions are accurate and thuscontribute errors to the Viterbi algorithm in making the maximumlikelihood decisions. It can also be shown that to correct thissituation, one needs to slightly modify the Viterbi algorithm andinclude artificial symbols outside the boundary of FIG. 2. FIG. 9 showsthe resulting configuration of the artificial symbols and the allowedsymbols. Each of these artificial symbols is notated with a superscriptof an asterisk. It can be seen that FIG. 9 is identical to FIG. 2 exceptthat the former includes outside the boundary eight artificial symbolson each side thereof and thus a total of thirty-two such symbols.

Based on FIG. 9 as the aforementioned predetermined configuration, whena decoder input represents a symbol which is outside the boundary, theViterbi algorithm would, in a conventional manner, identify a number ofthe artificial symbols as ones of the tentative decisions. However, theartificial symbols thus identified are not the allowed symbols whichbit-to-symbol converter 177 could possibly generate. This being so, itcan be shown that these identified artificial symbols ought to beconverted to certain allowed symbols associated therewith and treated asthough the latter were identified. FIG. 9 shows this association usingidentical pairs of subset identifications and subscripts, which arearbitrarily numbered. For example, artificial symbol h₀ * is associatedwith allowed symbol h₀ ; c₁ * is associated with c₁ ; and so on and soforth. The present Viterbi algorithm in this particular embodiment ismodified to accommodate the above-described conversion, which may becarried out, for example, by looking up a predetermined conversiontable.

Turning to a third embodiment which is virtually identical to theforegoing second embodiment, in particular, the decoding circuitry inthis embodiment is structurally identical to aforementioned decodingcircuitry 880. That is, the nonlinear filter, here, also precedes thedecoder. However, unlike the second embodiment, the Viterbi algorithmand the predetermined configuration of the allowed symbols--FIG. 2--inthis particular embodiment are advantageously unmodified, therebyfurther simplifying the decoding process. It can be shown that thissimplification is accomplished in the present disclosed embodiment byincreasing the value of the aforementioned paramenter L associated withthe nonlinear filters. Specifically, these filters correspond tononlinear filters 505, 506 and the nonlinear filters in GPRP 629 anddecoding circuitry 660 of the first embodiment. Thus, unlike the firstand second embodiment in which L=12, the value of L in this particularembodiment exceeds 12--the GPRS bound. In fact, L is experimentallydetermined to be 14 in the present illustrative embodiment. However, theincrease in the value of L entails more power consumption in the GPRP ofthe transmitter, thereby decreasing the overall coding gain of DWNT 101in a power-limited environment. It can be shown that this increase inthe value of L from 12 to 14 results in a decrease of no more than 0.7dB in the coding gain using FIG. 2 as the signal constellation in thetransmitter. However, it can also be shown that this decrease in thecoding gain diminishes with increasing size of the signal constellation.

The foregoing merely illustrates the principles of the invention andthose skilled in the art will be able to devise numerous arrangementswhich, although not explicitly shown or described herein, embody theprinciples of the invention. By way of example, but not limitation, somepossible variations and alternatives will now be described.

For example, the illustrative embodiments disclose the invention in thecontext of a DWNT used in an ISDN environment. However, the presentinvention is equally usable in a voiceband modem communicating on, e.g.,a voiceband telephone channel, at a bit rate of at least 19.2 kb/s,e.g., 24 kb/s or even higher.

The invention has been disclosed in the context of a circuit-orientedISDN environment. However, it can also be used to provide high-speeddata transmission in totally packetized non-ISDN environments, as well.It is, in addition, usuable for use not only in telephone local looptransmission, but other suitable environments. Thus, for example, a DWNTembodying the principles of the invention could be used tointerconnect--over a telephone local loop or other transmission loop--alocal area network and a wide area network; a telephone central officeand a local area network; a PBX and a central office, two PBXs, etc. Inaddition, in particular applications it may be advantageous to implementthe DWNT in a "data over voice" mode in which the spectrum of the DWNTline signal is positioned so as to leave room at the lower end of thefrequency spectrum for the insertion of an accompanying voice signal.

The invention has been disclosed using carrierless AM/PM. However, otherpassband transmission schemes, including non-carrierless schemes such asquadrature-amplitude modulation, can be used to implement the invention.Similarly, although the illustrative embodiments utilize atwo-dimensional modulation scheme, the invention can be implementedusing modulation schemes of any other desired dimensionality, including,for example, one, four or eight dimensions. Advantageously, amulti-dimensional modulated signal may be more robust in the presence ofparticular channel impairments than, say, a one-dimensional, e.g.,single sideband, modulated signal. In addition, as long as thecoordinates of the symbol in each dimension are dependent--that is, eachcoordinate is a function of all of the data bits that the symbolrepresents, rather than being an independent function of some subset ofthose bits--increasing the dimensionality of the symbols increases themargin against noise and various channel impairments. Indeed, theimproved receiver error performance may be sufficiently significant tomake worthwhile the added implementational complexity of using, say,four or eight dimensions.

The invention has been illustrated in the context of a networktermination which operates at 480 kb/s. However, it could be used atlower bit rates, e.g., 160 kb/s, or higher bit rates, e.g., 1.544 Mb/sif this were found to be desirable.

All in all, we believe that Nyquist rate echo cancellation, such asshown in FIG. 1, is probably the technically superior approach for aDWNT. From a commercial standpoint, however, symbol rate echocancellation may be the preferred approach, particularly at 1.544 Mb/s,until the cost of very high speed A/D converters comes down.

The illustrative embodiments disclose the invention in the context oftransmission over a two-wire loop. An alternative, however, is to use afour-wire loop, i.e., a separate two-wire loop for each direction oftransmission, in which case, of course, no echo cancellation would beneeded.

Finally, the invention is disclosed herein in a form in which thevarious signal processing functions are performed by discrete functionalblocks. However, any one or more of these functions could equally wellbe performed by one or more appropriately programmed microprocessors,microcoded digital signal processing chips, etc.

We claim:
 1. Apparatus for transmitting a data signal which representsinformation, said data signal being corrupted by noise which issubstantially colored after propagating through a communications medium,said apparatus comprisingmeans for encoding said information using acode, the utilized code providing the encoded information havingimproved immunity to white noise relative to the uncoded information,and means for nonlinearly processing said encoded information in such amanner that distortion associated with subsequent whitening of saidnoise in receiver apparatus is reduced.
 2. The apparatus of claim 1wherein said code is a trellis code.
 3. The apparatus of claim 1 whereinsaid processing means employs generalized partial response signaling. 4.The apparatus of claim 3 wherein a parameter L is associated with saidprocessing means, the value of said parameter L being at least ageneralized partial response signaling bound.
 5. A method fortransmitting a data signal which represents information, said datasignal being corrupted by noise which is substantially colored afterpropagating through a communications medium, said method comprising thesteps ofencoding said information using a code, the utilized codeproviding the encoded information having improved immunity to whitenoise relative to the uncoded information, and nonlinearly processingsaid encoded information in such a manner that distortion associatedwith subsequent whitening of said noise in receiver apparatus isreduced.
 6. The method of claim 5 wherein said code is a trellis code.7. The method of claim 5 wherein said processing step employsgeneralized partial response signaling.
 8. The method of claim 7 whereina parameter L is associated with said processing step, the value of saidparameter L being at least a generalized partial response signalingbound.